Question

Is this function continuous or discrete? How far can you get on 20 gallons? What is the domain and range of this function? How many gallons to get 500 miles? Where do the labels on the graph go?

Answer 1

Step-by-step explanation

The equation of the function can be represented as shown as follows:

`G(m)=12m`

-This function is discrete.

-If we have 20 gallons, we can obtain the number of miles by plugging in the value into the equation, as shown as follows:

`20=12m`

Dividing both sides by 12:

`(20)/(12)=m`

Simplifying:

`(5)/(3)=m`

We can make 1.67 miles with 20 gallons.

-The domain of the function are all the Real Numbers and the Range are also the Real numbers.

-Finally, drawing the graph of the function:

The points of the table are the following:

Gallons Miles

2 24

4 48

6 72

8 96

-We can get the number of gallons needed to, make 500 miles by plugging the value 500 into the equation, as shown as follows:

`500=12m`

Isolating m:

`(500)/(12)=m`

Simplifying:

`41.7=m`

The number of gallons to make 500 miles is equal to 41.7 gallons

Finally, labeling the graph: